Solve sqrt{3x-4}=sqrt{4x-14}

$$\sqrt{ 3x-4 } = \sqrt{ 4x-14 }$$

Solve for x

$$x=10$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3x-4}\right)^{2}=\left(\sqrt{4x-14}\right)^{2}$$

Calculate \sqrt{3x-4} to the power of 2 and get 3x-4.

$$3x-4=\left(\sqrt{4x-14}\right)^{2}$$

Calculate \sqrt{4x-14} to the power of 2 and get 4x-14.

$$3x-4=4x-14$$

Subtract 4x from both sides.

$$3x-4-4x=-14$$

Combine 3x and -4x to get -x.

$$-x-4=-14$$

Add 4 to both sides.

$$-x=-14+4$$

Add -14 and 4 to get -10.

$$-x=-10$$

Multiply both sides by -1.

$$x=10$$

Substitute 10 for x in the equation \sqrt{3x-4}=\sqrt{4x-14}.

$$\sqrt{3\times 10-4}=\sqrt{4\times 10-14}$$

Simplify. The value x=10 satisfies the equation.

$$26^{\frac{1}{2}}=26^{\frac{1}{2}}$$

Equation \sqrt{3x-4}=\sqrt{4x-14} has a unique solution.

$$x=10$$